Sparse Approximations of 3D Mesh Geometry Using Frames as Overcomplete Dictionaries

Abstract

This paper presents a novel method for creating a frame, to be used as an over complete dictionary for the progressive compression of 3D mesh geometry. The frame is computed from redundant linear combinations of the eigenvectors of a mesh Laplacian matrix, and atoms are selected by a Matching Pursuit algorithm. Experimental results show that a sparser representation of a given mesh geometry can be obtained with the frame than by decomposition of the mesh geometry onto an orthogonal basis. The proposed frame also has other desirable properties, including directionality and orient ability of the atoms, and the ability to be applied directly to a manifold mesh with arbitrary topology and connectivity type.